Why do you assign her the title of Crown Princess? While I understand that the Duke of Aosta now claims headship of the House of Savoy, the Prince of Naples is generally still recognized as Head of the House and direct heir of his father the last King of Italy.
Neither gentleman enjoys an especially pristine reputation but there is no mechanism to remove Naples and Venice from the succession and replace them with Aosta and his line.

Mr.Vittorio-Emanuele of Savoy lost automatically his titles( and his dynastic rights) because of his marriage without a royal consent. His son, Mr.Emanuele-Filiberto of Savoy, had never obtained a royal decree for any title.
Since the death of King Umberto II, The Head of the Royal House of Savoy is HRH Prince Amedeo of Savoy (Duke of Savoy) and Crown Prince HRH Prince Aimone of Savoy (Duke of Aosta and of Puglia).
How could we call the wife of the Crown Prince if not Crown Princess?

Did Italy even use the title of Crown Prince during the monarchy?
If Aosta is the "legitimate" heir to the non-existent monarchy why did it take him so long to press his claims?
Like so many fallen monarchies these multiple claimants make them and their supporters look silly. If they cannot agree amongst themselves how can they expect their supporters to even think that monarchy would be a unifying thing for the nation.

Until 1946 The Heir to the Throne was called Crown Prince.
Italy has only one Head of the Royal Family respecting the Laws of the House of Savoy.
Crown Prince Aimone is very respected in the country even if he is less known than his father.

Well since his father Aosta never had the title of king and does not use the title of king, and his use of it would be debatable at best, it seems rather odd to assign the son the title of Crown Prince.

It just seems very odd for people to give someone a title such as "Crown Prince" that they do not even use themselves. It would be laughable for Amadeo to go around calling himself King and for Amione to then call himself the Crown Prince.

It seems the Italians are following the French route with multiple claimants to a non-existant throne

Even though the two branches of the House of Savoy are in dispute, the Duke of Aosta has never used the title of 'Crown Prince' and neither has his son. I think it more an affectation by some over-zealous supporters.

Crown Prince Aimone is very respected in the country even if he is less known than his father.

I'd rather say that Aimone is virtually unknown in Italy. And I wouldn't say he is very respected in the country, given that in the country practically nobody knows him; maybe he is very respected in his circles, but not among the general public.

Is is rather true that many Italians do not know HRH Crown Prince Aimone of Savoy very well because he is not very present in Television or in the newspapers. He is very dedicated to his Family and to his work for the Pirelli Group.

The main branch of the Savoy family is followed by the media, because - one may like it or not - they are the ones who made the country, although the Aosta's family male members gave their great contribution as soldiers.
Amedeo had his share of scandals as well: he cheated on both wives; has had out of the wedlock children (Ginevra, the daughter he has with Kyara Van Ellinkhuizen, is not his only love child...) He's less talked about, because he's not the descendant of the former King, and that's all. It has nothing to do with their jobs or whatever...
Besides any single human being has his/hes own character and peculiarities, which doesn't mean that a person is bad because he/she works in the show-biz.

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